In some appropriate units, time \((t)\) and position \((x)\) relation of a moving particle is given by \(t=x^2+x. \) The acceleration of the particle is:
| 1. | \(+\dfrac{2}{(x+1)^3}\) | 2. | \(+\dfrac{2}{(2x+1)}\) |
| 3. | \(-\dfrac{2}{(x+2)^3}\) | 4. | \(-\dfrac{2}{(2x+1)^3}\) |
Subtopic: Non Uniform Acceleration |
Level 3: 35%-60%
NEET - 2025
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A model for the quantized motion of an electron in a uniform magnetic field \(B\) states that the flux passing through the orbit of the electron is \(n(h/e)\) where \(n\) is an integer, \(h\) is Planck's constant and \(e\) is the magnitude of the electron's charge. According to the model, the magnetic moment of an electron is its lowest energy state will be (\(m\) is the mass of the electron):
| 1. | \(\dfrac{heB}{\pi m}\) | 2. | \(\dfrac{heB}{2\pi m}\) |
| 3. | \(\dfrac{he}{\pi m}\) | 4. | \(\dfrac{he}{2\pi m}\) |
Subtopic: Magnetic Moment |
Level 3: 35%-60%
NEET - 2025
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A microscope has an objective of focal length \(2~\text{cm},\) eyepiece of focal length \(4~\text{cm}\) and the tube length of \(40~\text{cm}.\) If the distance of distinct vision of eye is \(25~\text{cm},\) the magnification in the microscope is:
| 1. | \(150\) | 2. | \(250\) |
| 3. | \(100\) | 4. | \(125\) |
Subtopic: Simple & Compound Microscope |
Level 3: 35%-60%
NEET - 2025
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There are two inclined surfaces of equal length \((L)\) and same angle of inclination \(45^\circ\) with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes \(2\) times as much time to slide down on rough surface than on the smooth surface. The coefficient of kinetic friction \((\mu_k)\) between the object and the rough surface is close to:
| 1. | \(0.5\) | 2. | \(0.75\) |
| 3. | \(0.25\) | 4. | \(0.40\) |
Subtopic: Friction |
52%
Level 3: 35%-60%
NEET - 2025
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A full wave rectifier circuit with diodes \((D_1)\) and \((D_2)\) is shown in the figure. If input supply voltage \(V_{\text{in}}=220\sin(100\pi t)\) volt, then at \(t=15~\text{ms}\text{:}\)
| 1. | \(D_1\) and \(D_2\) both are forward biased |
| 2. | \(D_1\) and \(D_2\) both are reverse biased |
| 3. | Neither \(D_1\) nor \(D_2\) conducts at any time |
| 4. | \(D_1\) is reverse biased, \(D_2\) is forward biased |
Subtopic: Rectifier |
Level 3: 35%-60%
NEET - 2025
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A uniform rod of mass \(20~\text{kg}\) and length \(5\text{ m}\) leans against a smooth vertical wall making an angle of \(60^{\circ}\) with it. The other end rests on a rough horizontal floor. The friction force that the floor exerts on the rod is: (take \(g=10~\text{m/s}^2\) )
| 1. | \(200 ~\text{N}\) | 2. | \(200 \sqrt{3} ~\text{N}\) |
| 3. | \(100 ~\text{N}\) | 4. | \(100 \sqrt{3} ~\text{N}\) |
Subtopic: Torque |
Level 3: 35%-60%
NEET - 2025
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Two identical charged conducting spheres \(A\) and \(B\) have their centres separated by a certain distance. Charge on each sphere is \(q\) and the force of repulsion between them is \(F. \) A third identical uncharged conducting sphere is brought in contact with sphere \(A\) first and then with \(B \) and finally removed from both. New force of repulsion between spheres \( A\) and \(B \) (Radii of \(A\) and \(B \) are negligible compared to the distance of separation so that for calculating force between them they can be considered as point charges) is best given as:
| 1. | \(\dfrac{F}{2}\) | 2. | \(\dfrac{3 F}{8}\) |
| 3. | \(\dfrac{3 F}{5}\) | 4. | \(\dfrac{2 F}{3}\) |
Subtopic: Coulomb's Law |
65%
Level 2: 60%+
NEET - 2025
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Two cities \(X \) and \(Y\) are connected by a regular bus service with a bus leaving in either direction every \(T~\text{min}.\) A girl is driving scooty with a speed of \(60~\text{km/h}\) in the direction \(X\) to \(Y\) notices that a bus goes past her every \(30~\text{minutes}\) in the direction of her motion, and every \(10~\text{minutes}\) in the opposite direction. Choose the correct option for the period \(T\) of the bus service and the speed (assumed constant) of the buses.
| 1. | \(10 ~\text{min},~ 90~ \text{km/h}\) | 2. | \(15 ~\text{min},~ 120~ \text{km/h}\) |
| 3. | \(9 ~\text{min},~ 40~ \text{km/h}\) | 4. | \(25 ~\text{min},~ 100~ \text{km/h}\) |
Subtopic: Relative Motion in One Dimension |
53%
Level 3: 35%-60%
NEET - 2025
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A container has two chambers of volumes \(V_1=2~\text{litres} \) and \(V_2=3~\text{litres} \) separated by a partition made of a thermal insulator. The chambers contains \( n_1=5 \) and \( n_2=4 \) moles of ideal gas at pressures \(p_1=1~\text{atm} \) and \(p_2=2~\text{atm}, \) respectively. When the partition is removed, the mixture attains an equilibrium pressure of:
| 1. | \(1.4 ~\text{atm} \) | 2. | \(1.8 ~\text{atm} \) |
| 3. | \(1.3 ~\text{atm} \) | 4. | \(1.6 ~\text{atm} \) |
Subtopic: Ideal Gas Equation |
Level 3: 35%-60%
NEET - 2025
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De-Broglie wavelength of an electron orbiting in the \(n=2\) state of a hydrogen atom is close to: (given: Bohr radius \(=0.052~ \text{nm}\))
| 1. | \(1.67~ \text{nm}\) | 2. | \(2.67~ \text{nm}\) |
| 3. | \(0.067~ \text{nm}\) | 4. | \(0.67~ \text{nm}\) |
Subtopic: De-broglie Wavelength |
Level 3: 35%-60%
NEET - 2025
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